ALTERNATIVE CALCULATION OF THE PHYSICAL MASS OF THE ρ-MESON

Abstract

We have derived an expression for the physical mass and width of the ρ-meson in vacuum from its spectral function, calculated in the vector meson dominance model when a ρ0 meson couples to two virtual pions π+–π-. The propagator is computed after evaluating the ρ-meson self-energy. The real part of the ρ-meson self-energy is given by a divergent integral and needs to be regularized; the regularization is done by using a double subtracted dispersion relation. The result leads to a closed analytical expression which allow us to evaluate the spectral function in a closed way. The physical mass, defined as the magnitude of the four-momentum |k| for which the spectral function S(k2) attains its maximum value, is obtained, and it gives a value of 770 MeV, which is in total agreement with the reported experimental value of the ρ-meson mass.